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Quadratic Transformations
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Describe the transformations for each.
Terms in this set (14)
f(x) = -2(x + 3)² - 3
The parabola opens down; it's narrowed towards the line of symmetry; the vertex is (-3, -3).
f(x) = (1/2)(x - 2)² + 3
The parabola opens up; it widens away from the line of symmetry; the vertex is (2, 3).
f(x) = (-1/4)(x + 1)² - 4
The parabola opens down; it widens; the parent quadratic function is translated to the left 1 unit and down 4 units.
f(x) = -2(x - 3)² - 3
The parabola has a maximum with a vertex of (3, -3). The parabola is narrow because it changes faster than the parent quadratic function.
f(x) = 3(x + 2)² - 1
The parabola has a minimum with a vertex of (-2, -1). The parabola was dilated by narrowing; there was no reflection; and it was translated left 2 units and down 1 unit from the parent quadratic function.
f(x) = 4(x - 1)² - 3
The parabola opens up; it's narrowed towards the line of symmetry (it's speed is faster than the parent function); translates left one, down 3.
f(x) = .75 (x - 1)² - 3
The parabola opens up; it widens (the speed of the graph is slower than the parent function); the parent quadratic function is translated to the right 1 unit and down 3 units.
f(x) = -(x + 4)² - 3
The parabola opens down; the graph changes at the same speed as the parent quadratic function (does not narrow or widen); the vertex is (-4, -3); translates to the left 4 units and down 3 units.
f(x) = x² - 3
The parabola has a minimum with a vertex of (0, -3). The parabola was not dilated or reflected from the parent quadratic function; does not shift horizontally; only translated down 3 units.
f(x) = -(x + 3)²
The parabola opens down with no dilation (does not widen or narrow). It is translated to the left 3 units. Does not translate up or down.
f(x) = (x)² - 1
The parabola translates down 1, does not shift horizontally.
f(x) is the parent functions. What transformation happens in f(x) = 1/2(x - 1)² ?
The parabola narrows and shifts to the right one. Does not transform vertically.
f(x) is the parent function. What transformation happens in f(x) + 2 ?
The parabola translates up 2 units only.
f(x) is the parent function. What transformation happens in f(x) = (x + 2)² ?
The parabola translates left 2 units only.
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